In nonmalignant conditions, vaccines are not used to treat established disease, but rather to prevent disease from occurring in the first place. We believe that the best way to use vaccines to treat cancers like melanoma is to prevent disease from reoccurring after surgical treatment. We are studying the use of a peptide (protein fragment) vaccine that uses fragments of two proteins known to be on most melanoma cells. The fragments are known to be recognized by immune cells of patients who tissue type (similar to a blood type, also called HLA type) is HLA-A2+. In our study, patients with melanoma of the skin that has not spread to the lymph nodes but is thick enough to be concerning for reoccurrence (stage II melanoma) who are HLA-A2+ are given either the basic peptide vaccine or the vaccine plus GM-CSF injections. GM-CSF is a protein that stimulates the immune system and may improve the effectiveness of the vaccine, but the need for self-injections means that we don+t wish to use it unless it clearly improves the immune response to our vaccine. Injections are spread over a total of 6 months. Before and after vaccination, patients will have white blood cells removed by a procedure known as apheresis. The ability of these white cells to recognize and respond to the peptides before and after vaccination will be compared.